Question

The sum of the reciprocals of Arun's ages (in years) 3 years ago and
five years from now is 1/3 Find his present age.​

Answer 1

Answer:

okk its answer is

Step-by-step explanation:

7 years

mark me as brainliest

Answer 2

Let present age of Arun be x years,

3 years ago Arun's age = (x - 3) years

After 5 years Arun's age = (x + 5) years

According to the question,

The sum of the reciprocals of Arun's ages3 years ago and five years from now is 1/3

So,

$\dashrightarrow \sf \dfrac{1}{(x - 3)} + \dfrac{1}{(x + 5)} = \dfrac{1}{3}$

$\dashrightarrow \sf \dfrac{(x + 5) + (x - 3)}{(x - 3)(x + 5)} = \dfrac{1}{3}$

$\dashrightarrow \sf (x - 3)(x + 5) = 6(x + 1)$

$\dashrightarrow \sf {x}^{2} + 2x - 15 = 6x + 6$

$\dashrightarrow \sf {x}^{2} - 4x - 21 = 0$

Now, split the middle terms,

$\dashrightarrow \sf {x}^{2} - 7x + 3x - 21 = 0$

$\dashrightarrow \sf x(x - 7) + 3(x -7) = 0$

$\dashrightarrow\sf (x -7)(x + 3) = 0$

$\dashrightarrow \sf x = 7 \: or \: - 3$

Ago cannot be negative so,

x = 7

Hence, the Present age of Arun is 7 years